Faster Two Dimensional Pattern Matching with Rotations

The most efficient currently known algorithms for two dimensional matching with rotation have a worst case time complexity of O(n 2 m 3), where the size of the text is n 2 and the size of the pattern is m 2. In this paper we present two algorithms for the two dimensional rotated matching problem whose running time is O(n 2 m 2). The preprocessing time of the first algorithms is O(m 5) and the preprocessing time of the second algorithm is O(m 4).

[1]  Esko Ukkonen,et al.  A Rotation Invariant Filter for Two-Dimensional String Matching , 1998, CPM.

[2]  Theodore P. Baker A Technique for Extending Rapid Exact-Match String Matching to Arrays of More Than One Dimension , 1978, SIAM J. Comput..

[3]  Gonzalo Navarro,et al.  Optimal Exact and Fast Approximate Two Dimensional Pattern Matching Allowing Rotations , 2002, CPM.

[4]  Alfred V. Aho,et al.  Efficient string matching , 1975, Commun. ACM.

[5]  Wojciech Rytter,et al.  Text Algorithms , 1994 .

[6]  Gonzalo Navarro,et al.  An Index for Two Dimensional String Matching Allowing Rotations , 2000, IFIP TCS.

[7]  V AhoAlfred,et al.  Efficient string matching , 1975 .

[8]  Zvi Galil,et al.  Alphabet-Independent Two-Dimensional Witness Computation , 1996, SIAM J. Comput..

[9]  Gad M. Landau,et al.  Two-dimensional pattern matching with rotations , 2004, Theor. Comput. Sci..

[10]  Roberto Grossi,et al.  On the Construction of Classes of Suffix Trees for Square Matrices: Algorithms and Applications , 1995, Inf. Comput..

[11]  Moshe Lewenstein,et al.  Real scaled matching , 2000, SODA '00.

[12]  M. Farach Optimal suffix tree construction with large alphabets , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[13]  Gad M. Landau,et al.  Fast Parallel and Serial Multidimensional Aproximate Array Matching , 1991, Theor. Comput. Sci..

[14]  Gad M. Landau,et al.  Efficient pattern matching with scaling , 1990, SODA '90.

[15]  Gad M. Landau,et al.  Pattern matching in a digitized image , 1992, SODA '92.

[16]  Amihood Amir,et al.  Two-Dimensional Dictionary Matching , 1992, Inf. Process. Lett..

[17]  M. Fischer,et al.  STRING-MATCHING AND OTHER PRODUCTS , 1974 .

[18]  Gary Benson,et al.  Alphabet independent two dimensional matching , 1992, STOC '92.

[19]  Dan Gusfield,et al.  Algorithms on Strings, Trees, and Sequences - Computer Science and Computational Biology , 1997 .

[20]  R.S. Bird,et al.  Two Dimensional Pattern Matching , 1977, Inf. Process. Lett..

[21]  Esko Ukkonen,et al.  Combinatorial methods for approximate pattern matching under rotations and translations in 3D arrays , 2000, Proceedings Seventh International Symposium on String Processing and Information Retrieval. SPIRE 2000.

[22]  Moshe Lewenstein,et al.  Real Two Dimensional Scaled Matching , 2003, WADS.